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Kevin Ryde > Math-NumSeq > Math::NumSeq::Pronic

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Module Version: 72

# NAME

Math::NumSeq::Pronic -- pronic numbers

# SYNOPSIS

``` use Math::NumSeq::Pronic;
my \$seq = Math::NumSeq::Pronic->new;
my (\$i, \$value) = \$seq->next;```

# DESCRIPTION

The pronic numbers i*(i+1),

```    0, 2, 6, 12, 20, 30, ...
starting i=0```

These are twice the triangular numbers, and half way between the perfect squares.

# FUNCTIONS

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

`\$seq = Math::NumSeq::Pronic->new ()`

Create and return a new sequence object.

## Iterating

`\$seq->seek_to_i(\$i)`

Move the current sequence position to `\$i`. The next call to `next()` will return `\$i` and corresponding value.

`\$seq->seek_to_value(\$value)`

Move the current sequence position so that `next()` will give `\$value` on the next call, or if `\$value` is not a pronic number then the next pronic above `\$value`.

## Random Access

`\$value = \$seq->ith(\$i)`

Return `\$i*(\$i+1)`.

`\$bool = \$seq->pred(\$value)`

Return true if `\$value` is a pronic number, ie. i*(i+1) for some i.

`\$i = \$seq->value_to_i_ceil(\$value)`
`\$i = \$seq->value_to_i_floor(\$value)`

Return the `\$i` index of `\$value`, rounding up or down if `\$value` is not a pronic number.

`\$i = \$seq->value_to_i_estimate(\$value)`

Return an estimate of the i corresponding to `\$value`. value=i*(i+1) is inverted by

`    \$i = int( (sqrt(4*\$value + 1) - 1)/2 )`

http://user42.tuxfamily.org/math-numseq/index.html

Copyright 2010, 2011, 2012, 2013, 2014 Kevin Ryde

Math-NumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.

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